If a polynomial "contains", in a multiplicative sense, a factor 
, then the polynomial has a zero at 
.
So, you polynomial must contain at least the following:
If you multiply them all, you get
Now, if you want the polynomial to be zero only and exactly at the four points you've given, you can choose every polynomial that is a multiple (numerically speaking) of this one. For example, you can multiply it by 2, 3, or -14.
If you want the polynomial to be zero at least at the four points you've given, you can multiply the given polynomial by every other function.
There are 2 unknown terms in this problem
the amount of cement the first team received is termed as 'x' hereafter
the cement the second team received is termed as 'y'
the first team received 50 kg less, the 1st equation is as follows;
x = y - 50 after rearranging
1) x-y = -50
for every hour 150 kg and 200 kg were used by the two teams separately
after three hours first team used up 150*3 = 450 kg
the second team used up 200 * 3 = 600 kg
however the first team had 1.5 times as much as second team had after three hours.
After three hours;
the amount second team had leftover was y - 600
the amount first team had leftover was x - 450
the amount the second team had ,multiplied by 1.5 is equal to what the first team had
we can build the 2nd equation using this information
1.5 * (y-600) = x-450
1.5y - 900 = x - 450
rearrange the equation,
1.5y - x = -450 +900
2) 1.5y - x = 450
add 1st and 2nd equations to eliminate x
1) + 2) (x - y = -50) + (1.5y - x = 450)
1.5y - y = 450 -50
0.5y = 400
y = 400/ 0.5
y = 800 kg
substitute y = 800 in x = y - 50
x = 800 - 50
x = 750 kg
first team received 750 kg and second team received 800 kg
Answer: -12 x^2 - 3x + 27
In this question, there are two function of f(x) and g(x)
f(x)= -9 x^2 - 7x + 12
g(x)= 3x^2 -4x -15
The question is about f(x)- g(x). To answer this, you just need to replace the question with the function. Don't forget to apply the minus to all the product inside the function. The calculation would be:
f(x)- g(x)=
(-9 x^2 - 7x + 12) -(3x^2 -4x -15)=
-9 x^2 - 7x + 12 (-3x^2 +4x +15)=
-12 x^2 - 3x + 27
Interesting problem ...
The key is to realize that the wires have some distance to the ground, that does not change.
The pole does change. But the vertical height of the pole plus the distance from the pole to the wires is the distance ground to the wires all the time. In other words, for any angle one has:
D = L * sin(alpha) + d, where D is the distance wires-ground, L is the length of the pole, alpha is the angle, and 'd' is the distance from the top of the (inclined) pole to the wires:
L*sin(40) + 8 = L*sin(60) + 2, so one can get the length of the pole:
L = (8-2)/(sin(60) - sin(40)) = 6/0.2232 = 26.88 ft (be careful to have the calculator in degrees not rad)
So the pole is 26.88 ft long!
If the wires are higher than 26.88 ft, no problem. if they are below, the concerns are justified and it won't pass!
Your statement does not mention the distance between the wires and the ground. Do you have it?
By taking a look at 1.64, you can already tell the 1 will be the whole number in the fraction. So let's focus on .64.
0.64 is in the hundredths place value, so the denominator will be 100. The unsimplified fraction would be 1 64/100.
To put this in simplest form we must divide 64 and 100. Let's start off with 2.
64/2 = 32
100/2 = 50
Let's continue until we can not divide by 2 anymore.
32/2=16
50/2 = 25
We can no longer divide by 2, howver there is not other number we can divide by both 16 and 25 evenly.
The answer in simplest form is 1 16/25
